To find the solutions to the quadratic equation \( 2x^2 - 5x = 6 \), we will first rearrange the equation into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can apply the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \( a = 2 \), \( b = -5 \), and \( c = -6 \).
First, we find the discriminant (\( b^2 - 4ac \)):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now we calculate the two potential values for \( x \):
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
Next, we compute \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.544 \]
Thus, we have:
\[ x = \frac{5 \pm 8.544}{4} \]
Calculating the two solutions:
- For \( x = \frac{5 + 8.544}{4} \):
\[ x \approx \frac{13.544}{4} \approx 3.386 \]
- For \( x = \frac{5 - 8.544}{4} \):
\[ x \approx \frac{-3.544}{4} \approx -0.886 \]
Rounding to the nearest hundredth, the solutions are approximately:
- \( x \approx 3.39 \)
- \( x \approx -0.89 \)
From the provided options, the only possible solution is:
\[ \boxed{-0.89} \]